QCD matter
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Quark Matter refers to any of a number of phases of matter built out of quarks and gluons. These constituents of quark matter carry colour charges and interact through Quantum chromodynamics. The scale of this theory, ΛQCD is of the order of a few hundred MeV (ie, about 1012 K). In this article low temperature (or chemical potential) will mean energies lower than this.
Hot quark matter called the quark-gluon plasma is expected to have filled the universe till about 20 or 30 microseconds after the big bang. Some colder phases such as strange matter and colour superconductors have been conjectured as present day constituents of stars denser even than neutron stars. The normal phase of quark matter is what we see everywhere else. In this phase quarks are confined within hadrons, either by partnering with an anti-quark to make a meson, or by joining with two other quarks to build a baryon.
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Thermodynamics
QCD contains many flavours of quarks and no flavour changing interactions. Therefore quark flavours are conserved charges. As a result, one can use a chemical potential with respect to each flavour charge. At temperatures below and in the vicinity of the QCD scale, one needs only the chemical potentials for the up (u), down (d) and strange (s) flavours, because the remaining quark flavours are too heavy to participate in the dynamics. The physics implications are sometimes clearer if one instead uses chemical potentials for baryon number, electric charge and hypercharge.
The phase diagram of QCD matter contains three chemical potentials (μ) and the temperature (T). These are the intensive variables for the thermodynamics of quark matter. The corresponding extensive variables are baryon number, electric charge, hypercharge and the energy. With so many variables, the phase diagram can become complex, and allow for a large variety of phases.
(For relativistic matter the pressure is not an independent intensive variable. It is completely determined once the remaining intensive variables are specified. Particle production and annihilation processes make sure that in a relativistic theory the pressure adjusts to changes in the other intensive thermodynamic variables.)
Order parameters
In thermodynamics, phases are distinguished by order parameters. One order parameter for QCD is the quark condensate (sometimes called the chiral condensate). This tracks the change from normal (hadronic) matter to the quark-gluon plasma. Another order parameter that has been studied recently is the pion condensate. This is useful in tracking phase transitions between the normal phase with small number of baryons but large electric charge and another phase in which a pion-superfluid exists. Diquark condensates have been studied to locate the phase transition from normal to colour superconducting quark matter.
The phase diagram
Only a small part of the phase diagram of QCD has been explored uptil now. At small T and μ one has the normal phase. At high T but reasonably small μ one has the quark-gluon plasma phase. At small T, small baryon density but large charge density one has a pion superfluid phase. These have been verified through computations in lattice QCD.
Higher values of μ have been probed by other means (see the next section). These studies have revealed several different colour superconducting phases of QCD.
The equation of state
The equation of state is usually a relation between the extensive and the intensive variables of the theory. This has been constructed for quark matter with vanishing or small μ. A first order phase transition can be identified by a discontinuity in the equation of state called the latent heat.
Useful theoretical fictions
Exact theoretical studies of quark matter need to use lattice QCD. However, in various parts of the phase diagram, its use is hampered by the fermion doubling problem and the fermion sign problem. Since the study of quark matter is so complicated, theorists like to change the quark mass to create simpler models of quark matter which (they hope) still captures crucial aspects of the physics.
The quenched approximation
One such is the quenched approximation, where all quark masses are taken to be infinite. In such this approximation, quarks do not take part in the dynamics, but the transition from confinement to deconfinement can be easily studied.
The chiral limit
Another appproximation is to take the chiral limit, where all quarks masses are taken to be zero. In this limit the dynamics of gluons is unimportant. As a result, simple effective theories can be written down. Some widely used effective theories are the sigma model and the (nearly equivalent) Nambu Jona-Lasinio model. With the further approximation of taking a large number of colours, elegant schemes such as the 1/N expansion can be applied.
The AdS/CFT limit
A fairly new approximation is to adjoint to QCD other particles which are related to quarks by supersymmetry. In suitably chosen such theories, if the chiral and large N limits are also taken, then a string theory motivated approximation called the AdS/CFT correspondence can be applied.
Weak coupling theory
The most widely used approximation is the weak-coupling approximation. Due to the property of asymptotic freedom that QCD enjoys, when T or μ is much larger than ΛQCD, the colour charge becomes weak. Then perturbation theory can be used to find the properties of quark matter.
See also
References and external links
- Reviews: 1999 (http://arxiv.org/pdf/hep-ph/9908360), 2001 (http://arxiv.org/pdf/hep-lat/0109034), 2003 (http://arxiv.org/pdf/hep-ph/0402115), 2005 (http://arxiv.org/pdf/hep-ph/0505073)
- The relativistic heavy ion collider (http://www.bnl.gov/rhic)
- The Indian Lattice Gauge Theory Initiative (http://theory.tifr.res.in/~sgupta/ilgti/)
Categories: Unsolved problems in physics | Particle physics | Quantum chromodynamics | Quark matter | Plasma physics | Phases of matter | Astrophysics
